# Learning PDEs on Helmholtz 3D a=3

Source: [Learning PDEs on Helmholtz 3D a=3](<https://www.sota2.com/research/sota/learning-pdes-on-helmholtz-3d-a-3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-26T09:11:59.375Z

Evaluation of models learning Partial Differential Equations (PDEs) on the Helmholtz 3D configuration with parameter a=3, measured by Relative L2 error.

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Learning PDEs |
| Dataset (including any stated split) | Helmholtz 3D a=3 |
| Metric | Relative L2 Error |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 6 of 6 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [Relative L2 Error](<https://www.sota2.com/research/sota/learning-pdes-on-helmholtz-3d-a-3.md?metric=Relative%20L2%20Error>): Lower is better; unit: SCALAR.

## Recorded results

| Method | Relative L2 Error | Result date | Report paper |
| --- | --- | --- | --- |
| Hermite-NGP | 0.0000609 | Not recorded | 6a15293cdbd7150506f7e0e3 |
| PirateNet | 0.00084 | Not recorded | 6a15293cdbd7150506f7e0e3 |
| INGP-FD | 0.00404 | Not recorded | 6a15293cdbd7150506f7e0e3 |
| SPINN | 0.0228 | Not recorded | 6a15293cdbd7150506f7e0e3 |
| PIG | 0.257 | Not recorded | 6a15293cdbd7150506f7e0e3 |
| PINN | 0.258 | Not recorded | 6a15293cdbd7150506f7e0e3 |

### Hermite-NGP

Relative L2 Error: 0.0000609. Result ID: 6a1563d7fbc373592c0d0a4b.

[Reporting paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

[Method origin paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

Recorded evaluation configuration: {"Model Scale":"Compact (Larger)"}. This record does not assert independent reproduction.

### PirateNet

Relative L2 Error: 0.00084. Result ID: 6a1563d7fbc373592c0d0a4c.

[Reporting paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5b6b1e209131ce9c82a9.md>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

### INGP-FD

Relative L2 Error: 0.00404. Result ID: 6a1563d7fbc373592c0d0a4d.

[Reporting paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa461e1e209131ce91df9b.md>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

### SPINN

Relative L2 Error: 0.0228. Result ID: 6a1563d7fbc373592c0d0a4e.

[Reporting paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa71121e209131cea4f149.md>)

[Implementation](<https://jwcho5576.github.io/spinn.github.io/>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

### PIG

Relative L2 Error: 0.257. Result ID: 6a1563d7fbc373592c0d0a50.

[Reporting paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa77771e209131cea7352f.md>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

### PINN

Relative L2 Error: 0.258. Result ID: 6a1563d7fbc373592c0d0a4f.

[Reporting paper](<https://www.sota2.com/research/paper/6a15293cdbd7150506f7e0e3.md>)

Recorded evaluation configuration: Not recorded. This record does not assert independent reproduction.

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